What is 4/15 plus 5/9? (Answer: 37/45)

Exact Answer

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Problem: What is 4/15 plus 5/9?
Formula / Expression: 4/15 + 5/9
Final Answer: 37/45
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 15 and 9 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 45 (which is smaller than their product 15 × 9 = 135, keeping the calculation simpler).
Working: LCD(15, 9) = 45

Step 2: Convert to Equivalent Fractions with Common Denominator 45
Multiply the numerator and denominator of 4/15 by 3, and multiply the numerator and denominator of 5/9 by 5 so both fractions share the common base 45.
Working: 4 × 3/15 × 3 = 12/45 and 5 × 5/9 × 5 = 25/45

Step 3: Add the Numerators
Now add the numerators (12 + 25 = 37) and keep the common denominator 45 unchanged.
Working: 12 + 25/45 = 37/45

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 37 and 45 is 1, confirming that 37/45 cannot be reduced further—it is already in its simplest irreducible form.
Working: 37/45

Step 5: Decimal & Percentage Representation
Dividing the numerator 37 by denominator 45 produces a repeating decimal (approximately 0.822222, or 82.2222%).
Working: 37 ÷ 45 = 0.822222 (82.2222%)

Key Values:
- Simplified Fraction: 37/45
- Mixed Number Form: 37/45
- Decimal Value: 0.822222
- Percentage: 82.2222%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-4-15-plus-5-9/
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4/15 + 5/9 = 37/45

Simplified Fraction

37/45

Mixed Number

Proper (37/45)

Decimal Value

0.822222

Percentage

82.2222%

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Step-by-Step Solution: 4/15 + 5/9

Step 1

Find the Least Common Denominator (LCD)

The denominators 15 and 9 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 45 (which is smaller than their product 15 × 9 = 135, keeping the calculation simpler).

LCD(15, 9) = 45

Step 2

Convert to Equivalent Fractions with Common Denominator 45

Multiply the numerator and denominator of 4/15 by 3, and multiply the numerator and denominator of 5/9 by 5 so both fractions share the common base 45.

4 × 3/15 × 3 = 12/45 and 5 × 5/9 × 5 = 25/45

Step 3

Add the Numerators

Now add the numerators (12 + 25 = 37) and keep the common denominator 45 unchanged.

12 + 25/45 = 37/45

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 37 and 45 is 1, confirming that 37/45 cannot be reduced further—it is already in its simplest irreducible form.

37/45

Step 5

Decimal & Percentage Representation

Dividing the numerator 37 by denominator 45 produces a repeating decimal (approximately 0.822222, or 82.2222%).

37 ÷ 45 = 0.822222 (82.2222%)

Visual Representation

The diagram below illustrates 4/15 plus 5/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`37/45`
Mixed Number Form	`37/45`
Decimal Form	`0.822222`
Percentage	`82.2222%`

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Frequently Asked Questions

What is 4/15 plus 5/9 as a fraction?

4/15 + 5/9 in simplest fraction form is 37/45.

What is 4/15 plus 5/9 as a decimal?

4/15 + 5/9 converted to a decimal is 0.822222.

What is 4/15 plus 5/9 as a percentage?

4/15 + 5/9 expressed as a percentage is 82.2222%.

Does 4/15 plus 5/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.822222...) because the denominator contains prime factors other than 2 and 5.